Abstract

It is shown that optical vortex beams can be generated from a non-vortex fundamental beam by an optical frequency conversion process taking place within a twisted nonlinear photonic crystal. This is done without any first-order (linear) refractive optics. Through such a proposed structure, all-optical switching of vortices with different helicities is made possible, as well as the simultaneous application of counter-rotating vortex beams of different frequencies.

© 2007 Optical Society of America

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  1. J. F. Nye and M. V. Berry, "Dislocations in Wave Trains," Proc. R. Soc. London Series A 336, 165-190 (1974).
    [CrossRef]
  2. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
    [CrossRef] [PubMed]
  3. J. Leach, E. Yao, and M. J. Padgett, "Observation of the vortex structure of a non-integer vortex beam," New J. Phys. 6, 71-78 (2004).
    [CrossRef]
  4. J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
    [CrossRef]
  5. M. E. J. Friese, H. Rubinsztein-Dunlop, J. Gold, P. Hagberg, and D. Hanstorp, "Optically driven micromachine elements, " Appl. Phys. Lett. 78, 547-549 (2001).
    [CrossRef]
  6. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001). quant-ph/0104070.
    [CrossRef] [PubMed]
  7. J. H. Lee, G. Foo, E. G. Johnson, and G. A. Swartzlander, Jr., "Experimental Verification of an Optical Vortex Coronagraph," Phys. Rev. Lett. 97, 053,901 (2006).
    [CrossRef]
  8. I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Optics of light beams with screw dislocations," Opt. Commun. 103, 422-428 (1993).
    [CrossRef]
  9. S. S. R. Oemrawsingh, J. A.W. van Houwelingen, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W. ’t Hooft, "Production and characterization of spiral phase plates for optical wavelengths," Appl. Opt. 43, 688-694 (2004).
    [CrossRef] [PubMed]
  10. T. J. Alexander, Y. S. Kivshar, A. V. Buryak, and R. A. Sammut, "Optical vortex solitons in parametric wave mixing," Phys. Rev. E 61, 2042-2049 (2000).
    [CrossRef]
  11. A. S. Desyatnikov, L. Torner, and Y. S. Kivshar, "Optical Vortices and Vortex Solitons," Prog. Opt. 47, 291-391 (2005).
    [CrossRef]
  12. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation -Tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
    [CrossRef]
  13. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between Light Waves in a Nonlinear Dielectric," Phys. Rev. 127, 1918-1939 (1962).
    [CrossRef]
  14. R. Lifshitz, A. Arie, and A. Bahabad, "Photonic Quasicrystals for Nonlinear Optical Frequency Conversion," Phys. Rev. Lett. 95, 133,901 (2005).
    [CrossRef]
  15. A. Ber?zanskis, A. Matijo?sius, A. Piskarskas, V. Smilgevi?cius, and A. Stabinis, "Conversion of topological charge of optical vortices in a parametric frequency converter," Opt. Commun. 140, 273-276 (1997).
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  18. G. Imeshev, M. Proctor, and M. M. Fejer, "Lateral patterning of nonlinear frequency conversion with transversely varying quasi-phase-matching gratings," Opt. Lett. 23, 673-675 (1998).
    [CrossRef]
  19. J. P. Torres, C. I. Osorio, and L. Torner, "Orbital angular momentum of entangled counter propagating photons," Opt. Lett. 29, 1939-1941 (2004).
    [CrossRef] [PubMed]
  20. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).
  21. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wavefront laser beams produced with a spiral phaseplate," Opt. Commun. 112, 321-327 (1994).
    [CrossRef]
  22. R. W. Boyd, Nonlinear Optics (Academic Press, 2003).
  23. Y. Nishida, H. Miyazawa, M. Asobe, O. Tadanaga, and H. Suzuki, "0-dB wavelength conversion using directbonded QPM-Zn : LiNbO3 ridge waveguide," IEEE Photonics Technol. Lett. 17, 1049-1051 (2005).
    [CrossRef]

2006

J. H. Lee, G. Foo, E. G. Johnson, and G. A. Swartzlander, Jr., "Experimental Verification of an Optical Vortex Coronagraph," Phys. Rev. Lett. 97, 053,901 (2006).
[CrossRef]

G. Swartzlander, "The Optical Vortex Lens," Opt. Photon. News 17, 39-43 (2006).
[CrossRef]

2005

Y. Nishida, H. Miyazawa, M. Asobe, O. Tadanaga, and H. Suzuki, "0-dB wavelength conversion using directbonded QPM-Zn : LiNbO3 ridge waveguide," IEEE Photonics Technol. Lett. 17, 1049-1051 (2005).
[CrossRef]

A. S. Desyatnikov, L. Torner, and Y. S. Kivshar, "Optical Vortices and Vortex Solitons," Prog. Opt. 47, 291-391 (2005).
[CrossRef]

R. Lifshitz, A. Arie, and A. Bahabad, "Photonic Quasicrystals for Nonlinear Optical Frequency Conversion," Phys. Rev. Lett. 95, 133,901 (2005).
[CrossRef]

2004

2002

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
[CrossRef]

2001

M. E. J. Friese, H. Rubinsztein-Dunlop, J. Gold, P. Hagberg, and D. Hanstorp, "Optically driven micromachine elements, " Appl. Phys. Lett. 78, 547-549 (2001).
[CrossRef]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001). quant-ph/0104070.
[CrossRef] [PubMed]

2000

T. J. Alexander, Y. S. Kivshar, A. V. Buryak, and R. A. Sammut, "Optical vortex solitons in parametric wave mixing," Phys. Rev. E 61, 2042-2049 (2000).
[CrossRef]

1998

1997

A. Ber?zanskis, A. Matijo?sius, A. Piskarskas, V. Smilgevi?cius, and A. Stabinis, "Conversion of topological charge of optical vortices in a parametric frequency converter," Opt. Commun. 140, 273-276 (1997).
[CrossRef]

1994

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wavefront laser beams produced with a spiral phaseplate," Opt. Commun. 112, 321-327 (1994).
[CrossRef]

1993

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Optics of light beams with screw dislocations," Opt. Commun. 103, 422-428 (1993).
[CrossRef]

1992

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation -Tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

1974

J. F. Nye and M. V. Berry, "Dislocations in Wave Trains," Proc. R. Soc. London Series A 336, 165-190 (1974).
[CrossRef]

1962

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between Light Waves in a Nonlinear Dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

’t Hooft, G. W.

Alexander, T. J.

T. J. Alexander, Y. S. Kivshar, A. V. Buryak, and R. A. Sammut, "Optical vortex solitons in parametric wave mixing," Phys. Rev. E 61, 2042-2049 (2000).
[CrossRef]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Arie, A.

R. Lifshitz, A. Arie, and A. Bahabad, "Photonic Quasicrystals for Nonlinear Optical Frequency Conversion," Phys. Rev. Lett. 95, 133,901 (2005).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between Light Waves in a Nonlinear Dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Asobe, M.

Y. Nishida, H. Miyazawa, M. Asobe, O. Tadanaga, and H. Suzuki, "0-dB wavelength conversion using directbonded QPM-Zn : LiNbO3 ridge waveguide," IEEE Photonics Technol. Lett. 17, 1049-1051 (2005).
[CrossRef]

Bahabad, A.

R. Lifshitz, A. Arie, and A. Bahabad, "Photonic Quasicrystals for Nonlinear Optical Frequency Conversion," Phys. Rev. Lett. 95, 133,901 (2005).
[CrossRef]

Basistiy, I. V.

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Optics of light beams with screw dislocations," Opt. Commun. 103, 422-428 (1993).
[CrossRef]

Bazhenov, V. Y.

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Optics of light beams with screw dislocations," Opt. Commun. 103, 422-428 (1993).
[CrossRef]

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wavefront laser beams produced with a spiral phaseplate," Opt. Commun. 112, 321-327 (1994).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Ber?zanskis, A.

A. Ber?zanskis, A. Matijo?sius, A. Piskarskas, V. Smilgevi?cius, and A. Stabinis, "Conversion of topological charge of optical vortices in a parametric frequency converter," Opt. Commun. 140, 273-276 (1997).
[CrossRef]

Berry, M. V.

J. F. Nye and M. V. Berry, "Dislocations in Wave Trains," Proc. R. Soc. London Series A 336, 165-190 (1974).
[CrossRef]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between Light Waves in a Nonlinear Dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Buryak, A. V.

T. J. Alexander, Y. S. Kivshar, A. V. Buryak, and R. A. Sammut, "Optical vortex solitons in parametric wave mixing," Phys. Rev. E 61, 2042-2049 (2000).
[CrossRef]

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation -Tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wavefront laser beams produced with a spiral phaseplate," Opt. Commun. 112, 321-327 (1994).
[CrossRef]

Curtis, J. E.

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
[CrossRef]

Desyatnikov, A. S.

A. S. Desyatnikov, L. Torner, and Y. S. Kivshar, "Optical Vortices and Vortex Solitons," Prog. Opt. 47, 291-391 (2005).
[CrossRef]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between Light Waves in a Nonlinear Dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Eliel, E. R.

Fejer, M. M.

G. Imeshev, M. Proctor, and M. M. Fejer, "Lateral patterning of nonlinear frequency conversion with transversely varying quasi-phase-matching gratings," Opt. Lett. 23, 673-675 (1998).
[CrossRef]

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation -Tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

Foo, G.

J. H. Lee, G. Foo, E. G. Johnson, and G. A. Swartzlander, Jr., "Experimental Verification of an Optical Vortex Coronagraph," Phys. Rev. Lett. 97, 053,901 (2006).
[CrossRef]

Friese, M. E. J.

M. E. J. Friese, H. Rubinsztein-Dunlop, J. Gold, P. Hagberg, and D. Hanstorp, "Optically driven micromachine elements, " Appl. Phys. Lett. 78, 547-549 (2001).
[CrossRef]

Gold, J.

M. E. J. Friese, H. Rubinsztein-Dunlop, J. Gold, P. Hagberg, and D. Hanstorp, "Optically driven micromachine elements, " Appl. Phys. Lett. 78, 547-549 (2001).
[CrossRef]

Grier, D. G.

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
[CrossRef]

Hagberg, P.

M. E. J. Friese, H. Rubinsztein-Dunlop, J. Gold, P. Hagberg, and D. Hanstorp, "Optically driven micromachine elements, " Appl. Phys. Lett. 78, 547-549 (2001).
[CrossRef]

Hanstorp, D.

M. E. J. Friese, H. Rubinsztein-Dunlop, J. Gold, P. Hagberg, and D. Hanstorp, "Optically driven micromachine elements, " Appl. Phys. Lett. 78, 547-549 (2001).
[CrossRef]

Imeshev, G.

Johnson, E. G.

J. H. Lee, G. Foo, E. G. Johnson, and G. A. Swartzlander, Jr., "Experimental Verification of an Optical Vortex Coronagraph," Phys. Rev. Lett. 97, 053,901 (2006).
[CrossRef]

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation -Tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

Kivshar, Y. S.

A. S. Desyatnikov, L. Torner, and Y. S. Kivshar, "Optical Vortices and Vortex Solitons," Prog. Opt. 47, 291-391 (2005).
[CrossRef]

T. J. Alexander, Y. S. Kivshar, A. V. Buryak, and R. A. Sammut, "Optical vortex solitons in parametric wave mixing," Phys. Rev. E 61, 2042-2049 (2000).
[CrossRef]

Kloosterboer, J. G.

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
[CrossRef]

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wavefront laser beams produced with a spiral phaseplate," Opt. Commun. 112, 321-327 (1994).
[CrossRef]

Leach, J.

J. Leach, E. Yao, and M. J. Padgett, "Observation of the vortex structure of a non-integer vortex beam," New J. Phys. 6, 71-78 (2004).
[CrossRef]

Lee, J. H.

J. H. Lee, G. Foo, E. G. Johnson, and G. A. Swartzlander, Jr., "Experimental Verification of an Optical Vortex Coronagraph," Phys. Rev. Lett. 97, 053,901 (2006).
[CrossRef]

Lifshitz, R.

R. Lifshitz, A. Arie, and A. Bahabad, "Photonic Quasicrystals for Nonlinear Optical Frequency Conversion," Phys. Rev. Lett. 95, 133,901 (2005).
[CrossRef]

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation -Tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001). quant-ph/0104070.
[CrossRef] [PubMed]

Matijo?sius, A.

A. Ber?zanskis, A. Matijo?sius, A. Piskarskas, V. Smilgevi?cius, and A. Stabinis, "Conversion of topological charge of optical vortices in a parametric frequency converter," Opt. Commun. 140, 273-276 (1997).
[CrossRef]

Miyazawa, H.

Y. Nishida, H. Miyazawa, M. Asobe, O. Tadanaga, and H. Suzuki, "0-dB wavelength conversion using directbonded QPM-Zn : LiNbO3 ridge waveguide," IEEE Photonics Technol. Lett. 17, 1049-1051 (2005).
[CrossRef]

Nishida, Y.

Y. Nishida, H. Miyazawa, M. Asobe, O. Tadanaga, and H. Suzuki, "0-dB wavelength conversion using directbonded QPM-Zn : LiNbO3 ridge waveguide," IEEE Photonics Technol. Lett. 17, 1049-1051 (2005).
[CrossRef]

Nye, J. F.

J. F. Nye and M. V. Berry, "Dislocations in Wave Trains," Proc. R. Soc. London Series A 336, 165-190 (1974).
[CrossRef]

Oemrawsingh, S. S. R.

Osorio, C. I.

Padgett, M. J.

J. Leach, E. Yao, and M. J. Padgett, "Observation of the vortex structure of a non-integer vortex beam," New J. Phys. 6, 71-78 (2004).
[CrossRef]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between Light Waves in a Nonlinear Dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Piskarskas, A.

A. Ber?zanskis, A. Matijo?sius, A. Piskarskas, V. Smilgevi?cius, and A. Stabinis, "Conversion of topological charge of optical vortices in a parametric frequency converter," Opt. Commun. 140, 273-276 (1997).
[CrossRef]

Proctor, M.

Rubinsztein-Dunlop, H.

M. E. J. Friese, H. Rubinsztein-Dunlop, J. Gold, P. Hagberg, and D. Hanstorp, "Optically driven micromachine elements, " Appl. Phys. Lett. 78, 547-549 (2001).
[CrossRef]

Sammut, R. A.

T. J. Alexander, Y. S. Kivshar, A. V. Buryak, and R. A. Sammut, "Optical vortex solitons in parametric wave mixing," Phys. Rev. E 61, 2042-2049 (2000).
[CrossRef]

Smilgevi?cius, V.

A. Ber?zanskis, A. Matijo?sius, A. Piskarskas, V. Smilgevi?cius, and A. Stabinis, "Conversion of topological charge of optical vortices in a parametric frequency converter," Opt. Commun. 140, 273-276 (1997).
[CrossRef]

Soskin, M. S.

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Optics of light beams with screw dislocations," Opt. Commun. 103, 422-428 (1993).
[CrossRef]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Stabinis, A.

A. Ber?zanskis, A. Matijo?sius, A. Piskarskas, V. Smilgevi?cius, and A. Stabinis, "Conversion of topological charge of optical vortices in a parametric frequency converter," Opt. Commun. 140, 273-276 (1997).
[CrossRef]

Suzuki, H.

Y. Nishida, H. Miyazawa, M. Asobe, O. Tadanaga, and H. Suzuki, "0-dB wavelength conversion using directbonded QPM-Zn : LiNbO3 ridge waveguide," IEEE Photonics Technol. Lett. 17, 1049-1051 (2005).
[CrossRef]

Swartzlander, G.

G. Swartzlander, "The Optical Vortex Lens," Opt. Photon. News 17, 39-43 (2006).
[CrossRef]

Swartzlander, G. A.

J. H. Lee, G. Foo, E. G. Johnson, and G. A. Swartzlander, Jr., "Experimental Verification of an Optical Vortex Coronagraph," Phys. Rev. Lett. 97, 053,901 (2006).
[CrossRef]

Tadanaga, O.

Y. Nishida, H. Miyazawa, M. Asobe, O. Tadanaga, and H. Suzuki, "0-dB wavelength conversion using directbonded QPM-Zn : LiNbO3 ridge waveguide," IEEE Photonics Technol. Lett. 17, 1049-1051 (2005).
[CrossRef]

Torner, L.

A. S. Desyatnikov, L. Torner, and Y. S. Kivshar, "Optical Vortices and Vortex Solitons," Prog. Opt. 47, 291-391 (2005).
[CrossRef]

J. P. Torres, C. I. Osorio, and L. Torner, "Orbital angular momentum of entangled counter propagating photons," Opt. Lett. 29, 1939-1941 (2004).
[CrossRef] [PubMed]

Torres, J. P.

van Houwelingen, J. A.W.

Vasnetsov, M. V.

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Optics of light beams with screw dislocations," Opt. Commun. 103, 422-428 (1993).
[CrossRef]

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001). quant-ph/0104070.
[CrossRef] [PubMed]

Verstegen, E. J. K.

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001). quant-ph/0104070.
[CrossRef] [PubMed]

Woerdman, J. P.

S. S. R. Oemrawsingh, J. A.W. van Houwelingen, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W. ’t Hooft, "Production and characterization of spiral phase plates for optical wavelengths," Appl. Opt. 43, 688-694 (2004).
[CrossRef] [PubMed]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wavefront laser beams produced with a spiral phaseplate," Opt. Commun. 112, 321-327 (1994).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Yao, E.

J. Leach, E. Yao, and M. J. Padgett, "Observation of the vortex structure of a non-integer vortex beam," New J. Phys. 6, 71-78 (2004).
[CrossRef]

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001). quant-ph/0104070.
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. Lett.

M. E. J. Friese, H. Rubinsztein-Dunlop, J. Gold, P. Hagberg, and D. Hanstorp, "Optically driven micromachine elements, " Appl. Phys. Lett. 78, 547-549 (2001).
[CrossRef]

IEEE J. Quantum Electron.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation -Tuning and tolerances," IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

IEEE Photonics Technol. Lett.

Y. Nishida, H. Miyazawa, M. Asobe, O. Tadanaga, and H. Suzuki, "0-dB wavelength conversion using directbonded QPM-Zn : LiNbO3 ridge waveguide," IEEE Photonics Technol. Lett. 17, 1049-1051 (2005).
[CrossRef]

Nature

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001). quant-ph/0104070.
[CrossRef] [PubMed]

New J. Phys.

J. Leach, E. Yao, and M. J. Padgett, "Observation of the vortex structure of a non-integer vortex beam," New J. Phys. 6, 71-78 (2004).
[CrossRef]

Opt. Commun.

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
[CrossRef]

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Optics of light beams with screw dislocations," Opt. Commun. 103, 422-428 (1993).
[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wavefront laser beams produced with a spiral phaseplate," Opt. Commun. 112, 321-327 (1994).
[CrossRef]

A. Ber?zanskis, A. Matijo?sius, A. Piskarskas, V. Smilgevi?cius, and A. Stabinis, "Conversion of topological charge of optical vortices in a parametric frequency converter," Opt. Commun. 140, 273-276 (1997).
[CrossRef]

Opt. Lett.

Opt. Photon. News

G. Swartzlander, "The Optical Vortex Lens," Opt. Photon. News 17, 39-43 (2006).
[CrossRef]

Phys. Rev.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between Light Waves in a Nonlinear Dielectric," Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Phys. Rev. A

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Phys. Rev. E

T. J. Alexander, Y. S. Kivshar, A. V. Buryak, and R. A. Sammut, "Optical vortex solitons in parametric wave mixing," Phys. Rev. E 61, 2042-2049 (2000).
[CrossRef]

Phys. Rev. Lett.

J. H. Lee, G. Foo, E. G. Johnson, and G. A. Swartzlander, Jr., "Experimental Verification of an Optical Vortex Coronagraph," Phys. Rev. Lett. 97, 053,901 (2006).
[CrossRef]

R. Lifshitz, A. Arie, and A. Bahabad, "Photonic Quasicrystals for Nonlinear Optical Frequency Conversion," Phys. Rev. Lett. 95, 133,901 (2005).
[CrossRef]

Prog. Opt.

A. S. Desyatnikov, L. Torner, and Y. S. Kivshar, "Optical Vortices and Vortex Solitons," Prog. Opt. 47, 291-391 (2005).
[CrossRef]

R. Soc. London Series A

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[CrossRef]

Other

R. W. Boyd, Nonlinear Optics (Academic Press, 2003).

C. N. Alexeyev, A. V. Volyar, and M. A. Yavorsky, "Intensely twisted elliptic optical fibres maintaining propagation of a single optical vortex," J. Opt.s A: Pure and Applied Optics 8, L5-L9 (2006). URL http://stacks.iop.org/1464-4258/8/L5.
[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).

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Figures (3)

Fig. 1.
Fig. 1.

Simulations of positively modulated nonlinear coefficient (left in each panel, while the background represents negatively modulated nonlinear coefficient) and the generated second harmonic amplitude (top right) and phase (bottom right) for a Gaussian pump beam. The linear coefficient (index of refraction) is assumed to be homogeneous. lc is the coherence length along the fields propagation direction. m is the phase-matching order. l is the topological charge. (a) m=1, l=1 (b) m=1, l=2 (c) m=1, l=5 (d) m=1, l=1.5 (e) m=3, l=3 (f) m=1, l=1 with a narrow beam waist.

Fig. 2.
Fig. 2.

Planar fabrication sampling for a vortex-generating ferroelectric nonlinear photonic crystal. The insets show a typical plate. (a) Stacking plates at the material polarization direction. (b) Stacking plates at the beams propagation direction.

Fig. 3.
Fig. 3.

Simulations of second harmonic amplitude (top) and phase (bottom) for a Gaussian pump beam within a Z-sampled structure. The phase matching order and topological charge are both 1. The sampling period is Δz=(2πk)/q. (a) q=3 (b) q=4 (c) q=14.

Equations (6)

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k 2 ω E 2 ω ( r ) z = 2 i ω 2 c 2 ( E ω ( r ) ) 2 d e f f , i j ( r ) e i Δ k z ,
E 2 ω ( z = L ) = κ 0 L g ( r ) e i Δ k z d z ,
E 2 ω ( z = L ) = κ G Δ k e i f ( x , y ) Δ k ,
g ( r ) = sign { cos [ Δ k / m ( z + l θ / Δ k ) ] } ,
g s ( r ) = ( g ( r ) · δ ( z n Δ z ) ) rect ( z / Δ z ) ,
E 2 ω n = sin c ( 1 n q 2 ) e i θ ( 1 n q ) ,

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